Let $\{x\}$ and $[x]$ denote the fractional part of $x$ and the greatest integer $\leq x$ respectively of a real number $x$. If $\int_0^n\{x\} d x, \int_0^n[x] d x$ and $10\left(n^2-n\right),(n \in N, n>1)$ are three consecutive terms of a G.P., then $n$ is equal to $\_\_\_\_$ .
